A Systematic Presentation of the Theory of Thin Airfoils in Non-Uniform Motion

Citation

Sears, William Rees (1938) A Systematic Presentation of the Theory of Thin Airfoils in Non-Uniform Motion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EM5X-CZ66. https://resolver.caltech.edu/CaltechETD:etd-06252004-134954

Abstract

The basic conceptions of the circulation theory of airfoils are reviewed briefly, and the mechanism by which a "wake" of vorticity is produced by an airfoil in non-uniform motion is pointed out. After a calculation of the induction effects of a wake vortex, it is shown how the lift and moment acting upon an airfoil in the two-dimensional case may be calculated directly from simple physical considerations of momentum and moment of momentum. Formulae for the lift and moment are then obtained which are applicable to all cases of motion of a two-dimensional thin airfoil in which the wake produced is approximately flat; i.e., in which the movement of the airfoil normal to its mean path is small.

The general results are applied first to the case of an oscillating airfoil, and vector diagrams giving the magnitudes and phase angles of the lift and moment are obtained. The results of a sudden change of angle of attack are then determined, and a general method for handling transient cases is set up. This method is applied to the calculation of the lift and moment acting on an airfoil entering sharp-edged and graded gusts. The case of a series of sinusoidal gusts is also considered.

A method of calculating the distribution of forces over the airfoil chord is then shown, and it is applied to the steady-state oscillation. The paper concludes with a discussion of the applicability of certain results to the explanation of observed phenomena beyond the stall.

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